1. ## Completing the square

given that $(x+b)(x+a)=(x+2)^2-9$, find the value of a and b

2. Originally Posted by Punch
given that $(x+b)(x+a)=(x+2)^2-9$, find the value of a and b
$x^2 + (a+b)x + ab = x^2 + 4x + 4 - 9$

compare the coefficients of x^2, x and constant. Then solve for a and b.

3. It's easier to factorise the RHS using DOTS

$(x + 2)^2 - 9 = (x + 2)^2 - 3^2$

$= (x + 2 + 3)(x + 2 - 3)$

$= (x + 5)(x - 1)$.

What do you think $a$ and $b$ are?